MRI is an imaging method which excites nuclear spin of an object set in a static magnetic field with a RF (radio frequency) signal having the Larmor frequency magnetically and reconstruct an image based on NMR (nuclear magnetic resonance) signals generated due to the excitation.
In the field of MRI, HFI (half Fourier imaging) method is known. The HFI method is an imaging method with compensating data in a region in which no data is acquired based on acquired k-space data by taking advantage of the complex symmetric of data in k-space.
As the conventional data processing for the HFI, HFI processing is performed. The HFI processing compensates data, which has not been acquired in k-space, based on acquired k-space data. Consequently, the whole data in k-space is generated.
Specifically, the HFI processing is performed in the following procedure. Here, it is assumed that the non-sampling region of k-space data is a high frequency region in the kz direction in k-space.
Firstly, two kinds of filter processing under a homodyne filter fh and a LPF (low pass filter) fl are performed in the kz direction in k-space. The homodyne filter fh is a filter which performs filter processing equivalent to processing for filling the non-sampling region with complex conjugate data. Specifically, the homodyne filter fh and the low pass filter fl are respectively performed on k-space data K to generate respective pieces of k-space data Kh(kx, ky, kz), Kl(kx, ky, kz) after the filter processing as shown by equations (1-1) and (1-2).K(kx,ky,kz)fh→Kh(kx,ky,kz)  (1-1)K(kx,ky,kz)fl→Kl(kx,ky,kz)  (1-2)
Next, 3D (three dimensional) FFT (Fast Fourier Transform) is performed to transform the respective pieces of the k-space data Kh(kx, ky, kz), Kl(Kx, ky, kz) into pieces of r-space data. Specifically, 3D FFT is performed on the pieces of the k-space data Kh(kx, ky, kz), Kl(kx, ky, kz) after the filter processing respectively to generate pieces of r-space data Vh(x, y, z), Vl(x, y, z) as shown by equations (2-1) and (2-2).FFT{Kh(kx,ky,kz)}→Vh(x,y,z)  (2-1)FFT{Kl(kx,ky,kz)}→Vl(x,y,z)  (2-2)
Next, phase correction processing and realization processing for removing errors are applied to the r-space data Vh after the homodyne filter processing fh. Specifically, the phase correction processing and the realization processing are performed to generate r-space data V(x, y, z) after the phase correction as shown by equation (3).V(x,y,z)=REAL{Vh(x,y,z)Vl*(x,y,z)/|Vl(x,y,z)|}  (3)
wherein VI* denotes the complex conjugation of VI and REAL( ) is the function to obtain the real part. Further, a weighted addition of the k-space data IFFT{V(x, y, z)} derived by 3D IFFT (Inverse Fast Fourier Transform) of the r-space data V(x, y, z) and the original k-space data K(kx, ky, kz) is performed with a weight coefficient α as shown by equation (4)K(kx,ky,kz)=αIFFT{V(x,y,z)}(1−α)K(kx,ky,kz)  (4)
Then, the result of the weighted addition is used as the k-space data K(kx, ky, kz) for calculating the r-space data V(x, y, z) again, and the HFI processing shown by equations (1-1), (1-2), (2-1), (2-2), (3) and (4) is repeated about 1 to 4 times in order to improve accuracy in compensating processing of k-space. That is, the filter processing, the 3D FFT, the phase correction processing and the weighted addition processing are repeated.
However, three dimensional HFI requires acquiring a larger amount of data compared to two dimensional. HFI, which leads to increase a period necessary for reconstruction. Improving accuracy in compensating processing of k-space requires repeating the HFI processing. Therefore, the period for the reconstruction becomes long by the number of repetitions of the HFI processing, which leads to increase a period of data processing.
An object of embodiments according to the present invention is to reduce a data processing period in three dimensional HFI.